Answer:
[tex]x=0,\;x=\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]\sqrt{x}=\sqrt{3}x[/tex]
Square both sides:
[tex]\implies \left(\sqrt{x}\right)^2= \left(\sqrt{3}x\right)^2[/tex]
[tex]\implies x= \left(\sqrt{3}\right)^2 \cdot \left(x\right)^2[/tex]
[tex]\implies x=3x^2[/tex]
Subtract x from both sides:
[tex]\implies x-x=3x^2-x[/tex]
[tex]\implies 0=3x^2-x[/tex]
[tex]\implies 3x^2-x=0[/tex]
Factor out the common term x:
[tex]\implies x(3x-1)=0[/tex]
Apply the zero-product property:
[tex]\implies x=0[/tex]
[tex]\implies 3x-1=0 \implies x=\dfrac{1}{3}[/tex]
Answer:
[tex] \sf \: x = \frac{1}{3} \: (or) \: x = 0[/tex]
Step-by-step explanation:
The equation given is,
→ √x = √3x
Now the value of x will be,
→ √x = √3x
→ x = (√3x)²
→ x = 3x²
→ 3x² = x
→ 3x² - x = 0
→ (3x - 1)(x) = 0
→ 3x - 1 = 0 || → x = 0
→ 3x = 0 + 1 || → [ x = 0 ]
→ 3x = 1 ||
→ [ x = 1/3 ] ||
These are the values of x.
Can someone solve the very first one under the pencil line solve that equation ASAP please
Answer:19.28 or 125/7
Step-by-step explanation:
first, replace all the a's with 1's, the b's with 2's, and the c's with 4's. you end up with (-3(1)+4(2)) ³/2(4)-1
then you would solve that until you get, (-3+8)³/8-1
then, (5)³/7
and once you've solved that you get 19.28 or 125/7
What is 3 to the 2 exponent?
Answer:
It would be 6 because the exponent is 2 so you multiply 3 twice which equals 6
Step-by-step explanation:
3 to the 2nd exponent is 3^2 = 9.
evaluate the expression
[Algebra, polynomials] I'd like help with further explanation with what the image is telling me. I understand that you find the GCF of each term, but for the question I don't know why the GCF of the exponents are 3. I thought 4 would be the GCF. I don't think I learned how to find GCF properly.
As for the second image, I just have no clue on how to do it. I don't want just the answer. Anyone good with math please help :)
Answer: For the GCF one, the GCF would be [tex]3y^{3}[/tex] because you are factoring from both [tex]15y^{4}[/tex] and [tex]12y^{3}[/tex], the reason it cannot be [tex]3y^{4}[/tex] is because that exponent value exceeds the exponent value of [tex]12y^{3}[/tex].
Step-by-step explanation:
So when you find a greatest common factor (GCF) you are basically trying to simplify the expression by extracting numbers to put it into its simplest form. The GCF of 15 and 12, is 3. And the GCF of the exponents would be [tex]y^{3}[/tex] .
What are the formula in coordinate geometry for Class 9?
The formula in coordinate geometry for Class 9 include distance formula, midpoint formula, section formula, equation of a line, slope of a line, equation of a circle, equation of a parabola, equation of an ellipse, equation of a hyperbola, area of a triangle, and area of a circle.
The distance formula is used to determine the distance between two points in a coordinate plane. The midpoint formula is used to find the midpoint between two points. The section formula is used to calculate the area of a triangle formed by three points. The equation of a line is used to define the line in terms of its slope and intercept. The slope of a line is used to calculate the angle of the line in relation to the x-axis. The equation of a circle is used to determine the equation of a circle with a given center and radius. The equation of a parabola is used to determine the equation of a parabola with a given focus and directrix. The equation of an ellipse is used to determine the equation of an ellipse with a given center and major and minor axes. In coordinate geometry the equation of a hyperbola is used to determine the equation of a hyperbola with a given center and asymptotes. The area of a triangle is used to find the area of a triangle given the three vertices. The area of a circle is used to find the area of a circle given the radius.
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Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 48 paintings to the local museum. Each of the 12 collectors will donate the same number of paintings How many paintings will Sergio have in his art collection after his donation?
Step-by-step explanation:
The question is a bit confusing, so I am going to reword it to what I assume it means, which is, “Sergio initially has “p” paintings. There are 12 art collectors total, including Sergio. All the art collectors together donate a total of 48 paintings, and each art collector donates the same number of paintings. How many paintings does Sergio have left?”
p = number of Sergio’s paintings at the start.
p-X = the number of Sergio’s paintings at the end.
48 = the total number of paintings donated by all art collectors
12 = number of art collectors
48/12 = 4 = the number of paintings that each art collector donated
4 = X = the number of paintings that Sergio donated
p-4 = the number of paintings Sergio has left (answer)
(My regrets if my understanding of the question was something other than the above.)
What equation is solved by the graphed systems of equations?
equation of first line -> y = x - 3
equation of second line -> y = 7x + 3
to get intersection, equate both equation
-> y = y
-> 7x + 3 = x - 3
What to do if the bases and exponents are different?
If the bases of two exponential expressions are different, they cannot be directly compared or combined.
THE BASE AND EXPONENTSYou can convert one of the bases to match the other by using logarithm properties. For example, if you want to compare or combine 2³ and 3², you can convert the base of one of them to match the other by using the logarithm property log3(3²) = 2, so 3² can be rewritten as 2^(log3(3²)) = 2².
If you want to add or subtract exponential expressions with different bases, you can convert one of the bases to match the other by using logarithm properties, then combine the exponents. For example, if you want to add 2³ and 3², you can convert the base of one of them to match the other by using the logarithm property log2(3) = 1.58496, so 3² can be rewritten as 2^(log2(3)*2) = 2^3.18992. Now you can add the two exponents: 2³ + 2^3.18992 = 2³ (1 + 2^0.18992).
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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 447 gram setting. Based on a 24 bag sample where the mean is 444 grams and the standard deviation is 10, is there sufficient evidence at the 0.1 level that the bags are underfilled or overfilled? Assume the population distribution is approximately normal.
Step 2 of 5: Find the value of the test statistic. Round your answer to three decimal places.
The value of the test statistic is given as 1.341
How to solve for the test statisticWe will solve for the test statistic through the use of the following data. We have the level of significance as 0.1, the standard deviation is given as 10, sample = 24, mean = 444
test statistic is solved with the formula: (x - µ )/SE =
hence we would have: ( 447 - 444 ) / 2.2371 = 1.341
Therefore the test statistics is given as 1.341
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A triangle has two sides measuring 8. 5 cm and 15 cm. What are the least and greatest whole number possibilities for the third side? enter your answers in the boxes.
The least whole number possibility for the third side is 8 cm. The greatest whole number possibility for the third side is 22 cm.
A triangle is a three-sided polygon. It is a geometric shape that has three edges and three vertices. Triangles can be classified based on their side lengths (such as equilateral, isosceles, or scalene) or based on the angles between their sides (such as acute, right, or obtuse). Triangles are a fundamental shape in geometry and are used in many branches of mathematics and physics. To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Using this rule, we can find the possible range of values for the third side of the triangle.
The least possible length of the third side would be:
8.5cm + 15cm - 15cm = 8.5cm
The greatest possible length of the third side would be:
(8.5cm + 15cm) - 1cm = 22.5cm
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Analyze and Persevere Susan bought
3 plants that cost $2.75 each. She wants
to buy 3 clay pots that cost $4.15 each.
If Susan had $20 to start, does she have
enough money to also buy the clay pots?
Explain. Bc
Using arithmetic operations it can be seen that if Susan had $20 to start, she does not have enough money to buy 3 clay pots pricing $4.15 each after buying plants costing $2.75 each. She can buy 2 clay pots.
What are the types of arithmetic operation?
The four basic arithmetic operations in Maths, for all real numbers, are -
Addition (Finding the Sum; ‘+’)
Subtraction (Finding the difference; ‘-’)
Multiplication (Finding the product; ‘×’ )
Division (Finding the quotient; ‘÷’)
Susan bought 3 plants that cost $2.75 each.
Using arithmetic operation of multiplication -
Total cost of the plants = number of plants bought × cost of each plant
Total cost of the plants = 3 × 2.75
Total cost of the plants = $8.25
Susan wants to buy 3 clay pots that cost $4.15 each.
Using arithmetic operation of multiplication -
Total cost of the clay pots = number of clay plots × cost of each clay pot
Total cost of the clay pots = 3 × 4.15
Total cost of the clay pots = $12.45
The total amount of money Susan has is $20.
She has already bought the plants.
So, the money left with her after buying the plants is -
Using arithmetic operation of subtraction -
Money left with Susan = Total money - Total cost of the plants
Money left with Susan = 20 - 8.25
Money left with Susan = $11.75
Therefore, Susan has enough money to buy only 2 clay pots and not 3.
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How do you write 3 exponents?
To write 3 exponents, you can use the following format: base^exponent.
An exponent is a small number that is written slightly above and to the right of a base number. The base is the number being multiplied, and the exponent tells you how many times the base is being multiplied by itself.
For example, to write 3 raised to the power of 2, you would write it as 3^2, which means 3 multiplied by itself 2 times, which is equal to 9.
It's important to note that the exponent is also known as the power, so 3^2, 3^3 and 3^4 are also read as 3 to the power of 2, 3 to the power of 3, 3 to the power of 4.
In summary, to write 3 exponents, you can use the format: base^exponent, where the base is the number being multiplied and the exponent tells you how many times the base is being multiplied by itself. In this case, 3^2, 3^3, and 3^4 represent 3 multiplied by itself 2, 3, and 4 times respectively.
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A rectangle has a perimeter of 38.6 kilometers and a base of 16.2 kilometers. What is the height?
The height of the rectangle is 3.1 kilometers.
What is the height?A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals which bisect each other . The perimeter of a rectangle is the distance round the rectangle. It is the sum of the four sides of the rectangle.
Perimeter of a rectangle = 2 x (height + width)
38.6 = 2 x (16.2 + height)
In order to determine the height, take the following steps:
38.6 / 2 = 16.2 + height
19.3 = 16.2 + height
height = 19.3 - 16.2 = 3.1 kilometers
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Find the perimeter of the given triangle
The perimeter of triangle DEF is 10.8 units.
What is perimeter of triangle?
The area around any two-dimensional figure determines its perimeter. We can calculate the perimeter of any closed shape by adding the lengths of its sides.
We are given that triangle ABC is similar to triangle DEF
So,
⇒AB/DE = BC/EF = AC/DF
We are given AB=5, BC=6 and DE = 3
Therefore,
⇒AB/DE = BC/EF
⇒5/3 = 6/EF
⇒EF = 3.6
Similarly, we are given AC =7
So,
⇒AB/DE = AC/DF
⇒5/3 = 7/DF
⇒DF = 4.2
Perimeter of triangle = DE + EF + DF
⇒Perimeter of triangle = 3 + 3.6 + 4.2
⇒Perimeter of triangle = 10.8 units
Hence, the perimeter of triangle DEF is 10.8 units.
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Which of the following tables represents a linear relationship that is also proportional? x y 0 3 3 6 6 9 x y 0 4 2 6 4 8 x y 0 0 6 3 12 6 x y 0 3 5 5 10 7
Choice B, with a y-intercept of 0, is the correct response and provides a table that depicts a linear and proportionate relationship that is
x y
0 0
2 1
4 2
What do you mean By graph Intercept function?
The graph's intercept is the location where the line or curve crosses the axis. The term "x-intercept" refers to a point that crosses the x-axis. The y-intercept is the location where a point crosses the y-axis. Here is a y-intercept illustration. Suppose the line y = x+ 3 exists. This graph's y-axis intersects at this location (0,3). So, the line y = x+3's y-intercept is (0,3). By changing Y to 0 and solving for X, you can always discover the X-intercept. Likewise, you may always solve for Y while holding X equal to 0 in the equation to determine the Y-intercept.To know more about intercept here
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7 of 8
→
The area of a circle, in terms of π, is 100
π m².
Find the value of the diameter.
d = 0
m
Answer:
look it up broski
Step-by-step explanation:
Shannon babysits and charges a flat fee of $10 plus $2 for very hour she babysits. She needs to make $72 this week. How many hours can Shannon babysit
Answer:
72 divided by 12 is 6 so 6 hours she needs to babysit
"subtract 7 from the sum of 34 and 3"
Answer: 30
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
(34 + 3) -7
37 - 7
30
What are coordinates Class 9?
A series of numbers known as coordinates can be used to display a point's precise location on a coordinate plane. Coordination Plane Definition. The intersection of the x-axis and y-axis, two perpendicular lines that create a 2D plane known as a coordinate plane.
Which coordinate system is used?There are three types of co-ordinates are:
(i) Cartesian co-ordinates
(ii) cylindrical co-ordinates
(iii) spherical co-ordinates
The Cartesian coordinate system is a prime example of a coordinate system. Two perpendicular lines are picked in the plane, and a point's coordinates are assumed to be the signed distances between the lines.
Coordinates are a pair of integers (also known as Cartesian coordinates), or occasionally a letter and a number, that identify a specific point on a grid, also known as a coordinate plane. Two axes, the x (horizontal) and y (vertical), and four quadrants make up a coordinate plane (vertical).
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Identify the center of dilation.
-8 -4
8
-4
-8
ty
8
x₁
X
Therefore , the ratio of the triangles ABC and XYZ's corresponding sides will therefore be the same.
Describe the triangle.A triangle is regarded as both a polygon since it has 4 elements or segments. It is a basic geometric form. Triangle ABC denotes a triangle having angles A, B, or C. Therefore, in Euclidean geometry, a single planes and square are produced whenever sides are not collinear. A triangle is a polygon if it has three parts and three corners. The points where a triangle's three sides come together are at its corners. The three triangular angles add up to 180 degrees.
Here,
An dilation is a change that produces an image that is smaller but still exactly the same shape also as original. A particular degree of stretching or contraction is possible for the initial figure.
We can see that in the problem, a 5x dilatation causes ABC to constrict to produce XYZ.
As a result, the triangles ABC or XYZ will have the same ratio of their corresponding sides.
A/B/C/D = A/C/X/Y/Z = 5
The ratio of the adjacent angles of the triangle ABC and XYZ will therefore be the same.
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-91x-13x= 276.50
Show work
Answer:
x = -2.65865384615
Step-by-step explanation:
-91x - 13x = 276.50
First, Combine Like Terms
-91x + (-13x) = -104x
-104x = 276.50
Second, divide
276.50 / -104 = x
x = -2.65865384615
Lines AE and GH are parallel in the image below. The image will be used to prove that the sum of the measures or the
interior angles of ACGH is 180°.
Which statement would be included in a proof of why m/C+m/G+mZH= 180
Angles F and C are congruent. An angle inside a form is called an interior angle.
What is interior angle?An angle inside a form is called an interior angle. The closed shape with vertices and sides is called a polygon. Every interior angle of a regular polygon is equal to every other interior angle. For instance, the inner angles of a square are all equal to the right angle, or 90 degrees. A set's interior is comprised of all of its open subsets. The area of a region that is "within" a given border is more often referred to as the interior of a geometric structure. For instance, the interior of a circle and a sphere, respectively, is a (open) disk. Interior angles are the angles created within or inside of a shape. In this case, the interior angles ABC, BCA, and CAB.
From the figure, it can be seen that Angles F and C are opposite angles. Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent .
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Angles F and C are congruent. An angle inside a form is called an interior angle.
What is interior angle?An angle inside a form is called an interior angle. The closed shape with vertices and sides is called a polygon. Every interior angle of a regular polygon is equal to every other interior angle. For instance, the inner angles of a square are all equal to the right angle, or 90 degrees.
A set's interior is comprised of all of its open subsets. The area of a region that is "within" a given border is more often referred to as the interior of a geometric structure. For instance, the interior of a circle and a sphere, respectively, is a (open) disk. Interior angles are the angles created within or inside of a shape. In this case, the interior angles ABC, BCA, and CAB.
From the figure, it can be seen that Angles F and C are opposite angles. Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent .
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Two identical springs (x and y) are stretched to different lengths and held there.
The illustration shows that (A) spring x has a higher elastic potential energy.
What is elastic potential energy?The energy that is stored when a force is used to deform an elastic object is known as elastic potential energy.
Until the force is released and the object springs back to its original shape, doing labor in the process, the energy is retained.
Kinetic energy is the power that an object has while in motion.
For instance, a stretched rubber band contains elastic potential energy because, when released, it will spring back to its resting position, converting the potential energy to kinetic energy.
So, according to the given image, spring x has more elastic potential energy.
Therefore, the illustration shows that (A) spring x has a higher elastic potential energy.
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Correct question:
Two identical springs ( x and y ) are stretched to different lengths and held there
Which of the following statements is true
A) spring x has more elastic potential energy
B) spring y has more elastic potential energy
C) spring x has more kinetic energy
D) spring y has more kinetic energy
. Temoso borrowed R1 000 from the bank for 3 years at 8% compound interes Without using a formula, calculate how much Temoso owes the bank at the end of three years.
Answer:initial balance: 1000
interest rate:8%
term 20 years
how often: never
The final balance is $4,926.8.
The total compound interest is $3,926.8.
Step-by-step explanation:
help me, please i need this by tomorrow and I'm in school
Answer:
1/3
Step-by-step explanation:
please give me brainliest
Answer:
4/16
Step-by-step explanation:
The answer is actually 4/16 because you cannot either divide or multiple by any number to get 4/16.
Solve the equation, and check your solution.
8.4+
8.4 = 1.4x
8.4+
—
= 1.4x +
= X
Complete the solution using inverse relationships.
8.4 = 1.4x
= 1.4x +
= X
-
(Type whole numbers or decimals.)
The solution to the equation 8.4 = 1.4x for the unknown variable x is 6.
How to solve equation?8.4 = 1.4x
divide both sides by the variable of x
x = 8.4 / 1.4
x = 6
Check:
8.4 = 1.4x
8.4 = 1.4(6)
8.4 = 8.4
Using inverse relationship
8.4 = k / 1.4
cross product
8.4 × 1.4 = k
11.76 = k
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Express 12^{\frac{1}{2}}12
2
1
in simplest radical form.
25/2 is simplest form of fraction.
In math, what is a fraction?
An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction.
Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other. The Latin word fraction, which meaning "to break," is where we get the English word fraction.
Fraction = 12 1/2
= 25/2
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Please help with this question ASAP
Answer:
x=8
Step-by-step explanation:
5(2)=10
4(2)=8
How do you write a polynomial function with factors?
So on provided question we cans ay that Take the common binomial into account. Note that when we multiply our response by itself, the original polynomial results.
what are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
here,
Group the first two terms first, followed by the last two terms. Remove a GCF from each each binomial. Take the common binomial into account. Note that when we multiply our response by itself, the original polynomial results.
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use pascal’s triangle to expand (z+1)^6
The expansion of (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z + 1
Pascal's Triangle:A type of number pattern is Pascal's Triangle. The triangle-shaped arrangement of integers known as Pascal's Triangle provides the coefficients for the expansion of any binomial statement.
The arrangement of the numerals creates a triangle when they are reflected. The number 1 is first placed at the top, and then the numbers are arranged in a triangle design.
The expansion of (x + y)ⁿ is is given by
(x + y)ⁿ = a₀xⁿ + a₁xⁿ⁻¹y + a₂xⁿ⁻²y² + … + a[tex]_{n -1}[/tex] xyⁿ⁻¹ + a[tex]_{n}[/tex]yⁿ
Here we have (z+1)⁶
Write out Pascal's triangle starting from 1 and up to 6 rows
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
So coefficients of expansion are 1, 6, 15, 20, 15, 6, and 1
(z+1)⁶ = (1)z⁶ + (6)z⁵(1)+ (15)z⁴(1)² + 20z³(1)³ + 15z²(1)⁴ + 6z¹(1)⁵ + (1)z⁰(1)⁶
=> (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z¹ + 1
Therefore,
The expansion of (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z + 1
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